Electronic method for generation of a single cycle of a trigonometric function



Jan. 16, 1962 P. c. PHILLIPS 3,017,580

ELECTRONIC METHOD FOR GENERATION OF A SINGLE CYCLE OF A TRIGONOMETRIC FUNCTION Filed Oct. 22, 1959 Emir Sh v IN V EN TOR. PAZ/Z (Pf /6//7' 0/1 PH/Z lPS WWW United tates 3,017,580 ELECTRONIC METHOD FOR GENERATION OF A SINGLE CYCLE OF A TRIGONOMETRHC FUNCTION The present invention relates to a method and means for production of a waveform according to a trigonometric function. The invention relates' more particularly to a method and means for production of sine or cosine waves for either a single cycle or an integral number of cycles, beginning at any arbitrary moment.

The method of this invention consists of establishing initial conditions in an inductance-capacitance (L-C) circuit by means of some external agency such as a voltage or current source, connecting or disconnecting the external agency which maintains the initial conditions thereby establishing a ringing condition in the L-C circuit, allowing the LC circuit to ring for one or more full cycles, then stopping the ringing after the cycle or cycles at which time the circuit has returned to the initial conditions, and holding these conditions by means of the external agency until another cycle is required. This invention is useful to achieve, for example, a circular sweep for a cathode ray tube display for specialized oscilloscope displays and modified radar A-scopes. The objects and uses of the method and the means embodying the present invention will be readily understood and appreciated when the description of the circuit is read and reference is made to the accompanying figures of the drawing in which:

FIGURE 1 illustrates an embodiment of the present inverciltion which produces a cosine waveform at the output, an

FIGURE 2 represents an embodiment of the invention which produces a sine waveform.

Referring to FIGURE 1, there is shown a triode 12 having a coupling capacitor 10 coupled between its grid and input terminal 9 for coupling a gating signal. The triode 12 has an anode coupled through a resistance to a source of positive voltage at terminal 8. It has a cathode coupled through cathode resistor 15 to a source of negative potential at terminal 28. One output terminal 21 is coupled to the cathode of triode 12 through the unidirectional means 13 the latter being oriented to have its high resistance in the direction from output terminal 21 to the cathode 22. Grid bias for triode 12 is achieved through resistor 11 coupled to terminal 7 where a suitable voltage is maintained. .The other output terminal 23 is coup'ed to the cathode of triode 12 through resistance 14 and through unidirectional means 17 in its conducting direction. Terminal 23 is also connected directly to ground. Inductor 16 and capacitor 18, which are coupled in common to output terminal 21, are coupled also to each other through the unidirectional means 17, capacitor 18 being coupled across the output terminals 21 and 23. An amplitude reference terminal 24 is connected through unidirectional means 20 in its high resistance direction to output terminal 21.

FIGURE 2 shows a triode 32 having an anode resistively coupled to a source of positive potential and a cathode coupled through variable resistor 35 to a source of negative potential 46. Again similar to FIGURE 1, a coupling capacitor 30 provides an input from terminal 29 for gating signals to be applied to the grid of triode 32 and a suitable biasing voltage is applied through resistor 31 from terminal 47. One output terminal 41 is connected through unidirectional means 33 in its conducting direction to the cathode of triode 32. The other output terminal 42 is connected through resistor 34 to the cathode of triode 32. Capacitor 38 is connected across the output terminals 4 1 and 42. Inductor 36 is connected from output terminal 41 to ground 39. Unidirectional means 37 is connected from capacitor 38 to ground 39, being oriented to provide a low resistance in that direction.

Both of the circuits represented in FIGURE 1 and FIGURE 2 take advantage of the fact that in the absence of damping, a resonant system having an inductance and capacitance passes through an identical set of conditions once each cycle. In the circuit of FIGURE 1, the cosine wave output is produced when the triode 12 is not conducting, at which time the circuit, including capacitor 18 and inductor 16, rings. Prior to cutoff of triode 12 current flows from the source of positive potential at terminal 8 through the triode and through resistor 15 to the source of negative potential at terminal 28.' There is accordingly a positive potential established at junction 22. This positive potential places a forward bias on unidirectional means 13 and a consequential positive potential is present on terminal 21. The amplitude of this potential is determined by a reference potential at terminal 24. Under these conditions the current through inductor 16 can stabilize at zero. When the tube 12 is shut oil by impression of a gating signal on the input terminal 9, the potential at junction 22 drops and due to the charge on capacitor 18 the unidirectional means 13 is reversed biased. Consequently, there is established a current from capacitor 18 through inductor 16, resistance 14, and resistance 15, to the source of negative potential at terminal 28. When the capacitor 18 is discharged by the current flowing through inductor 16 to the source of negative potential, current continues to flow during decay of the magnetic field around inductor 16 until a negative potential at the output terminal 21 is developed which has an amplitude approximately equal to the original positive potential. At this point capacitor 18 has accumulated a charge of the opposite polarity to its original charge, and begins to discharge. The effect of this charging and discharging of capacitor 18 (ringing of the circuit) is to produce a cosine waveform having limits of amplitude ranging approximately equally above and below the ground potential at 19. In order to stop the ringing when one cycle is complete, a detector, which is not a part of this invention, may be coupled to the output terminals 21 and 23 to terminate the gate at terminal 9 and permit resumption of conduction in the triode 12.

In FIGURE 2, the sine waveform is produced at the output when the triode 32 is conducting. To explain the operation of FIGURE 2 it is best to begin when the triode is not conducting. At this time there is established a flow of current from ground 39 through inductor 36, unidirectional means 33, and variable resistor 35, to the source of negative potential at terminal 28. At this time junction 43 is slightly negative, biasing unidirectional means 37 01f. Also, any charge on capacitor 38 can decay to zero through unidirectional means 33 and resistor 34. When the tube 32 is turned on, at any arbitrary time, by a gate applied to terminal 29, current flow through triode 32 and variable resistor 35 causes the potential at junction 43 to rise, causing the unidirectional means 33 to be reverse biased so that the current which had been established in inductor 36 while tube 32 was not conducting is directed into capacitor 38 while the magnetic field of inductor 36 collapses. Accordingly, there is a charge developed on capacitor 38. When the magnetic field of inductor 36 has collapsed, capacitor 38 begins to discharge through inductor 36 into ground 39.

The charging and discharging of capacitor 38 as the circuit rings causes a voltage on the output terminals 41 and 42 which varies from zero to a positive maximum, back to zero and then to a negative maximum and back to Zero, which is the sine waveform. Variable resistor 35 afi'ords means to adjust amplitude of the wave. To obtain only a single cycle, a detector which is not a part of this invention, may be connected to the output terminals 41 and 42 to determine when a cycle has been completed and cause the gate on the input terminal 29 to turn the tube 32 01f again.

For either the circuit of FIGURE 1 or FIGURE 2 the detection of phase Wt=21r to obtain either a single cycle or an integral number of cycles may be done most accurately by first amplifying and pipping the output appearing at the output terminals. The circuits may be allowed to ring for an integral number of cycles by counting down the pips for the desired number of complete cycles before causing the gate at the input to the triodes to terminate the ringing condition of the circuit. While the circuits shown in FIGURES 1 and 2 produce outputs of the sine and cosine waveforms, similar circuits within the scope of this invention could be devised which would produce other trigonometric waveforms. Accordingly, I wish the scope of this invention to be limited only by the following claims.

I claim:

1. An electronic means for generation of an integral number of cycles of a trigonometric function said means comprising: a switch tube coupled across a source of potential; an input to said switch tube for gating signals; a first unidirectional means having one terminal coupled to the cathode of said switch tube and the other terminal coupled to a common junction between first terminals of an inductance means and a capacitance means; a second unidirectional means having a first terminal means coupled to a second terminal of said inductance means and having a second terminal means coupled to a second terminal of said capacitance means and having one of said second terminals further coupled to a point of intermediate ground potential; resistance means coupled between said cathode and said second unidirectional means; output terminals coupled to said capacitance; and impedance means coupled between said cathode and a source of negative potential for establishing a desired amplitude of signals at said output terminals.

2. Electronic means for generation of an integral number of cycles of a cosine waveform said means comprising: a switching triode having an anode coupled to a source of positive potential, a grid adapted for coupling to a source of gating signals, and a cathode coupled to a source of negative potential; a first unidirectional means coupled between said cathode and a first output terminal, said unidirectional means having its low resistance direction from the cathode to said output terminal; a second output terminal coupled to ground, and serially coupled through a second unidirectional means and a first resistance to said cathode, said second unidirectional means having its low resistance in the direction from output terminal to cathode; an inductor coupled between said first output terminal and a junction between said second unidirectional means and said first resistance; a terminal for a reference voltage coupled through a third unidirectional means to said first output terminal; and a capacitor connected across said output terminals whereby a cosine waveform is produced at said output terminals when said switching triode is rendered nonconducting and is terminated when conduction is reestablished in said switching triode.

3. Electronic means for generation of an integral number of cycles of a sine waveform said means comprising: a switching triode having an anode coupled to a source of positive potential, a grid adapted for coupling to a source of gating signals, and a cathode coupled through a variable resistance to a source of negative potential; a first unidirectional means coupled between said cathode and a first output terminal, said unidirectional means having its low resistance direction from said output terminal to the cathode; a second output terminal coupled through a first resistor to the cathode; a second unidirectional means coupled between said second output terminal and ground, the low resistance being in the direction from said output terminal to ground; an inductor coupled from said first output terminal to ground; and a capacitor coup'ed across said output terminals whereby a sine waveform is produced at said output terminals when said switching triode is in a conducting condition being terminated when said triode is cut off.

References Cited in the file of this patent UNITED STATES PATENTS 2,610,294 Seddon Sept. 9, 1952 2,638,548 MacNichol May 12, 1953 2,724,776 Sherwin Nov. 22, 1955 2,741,701 Harris Apr. 10, 1956 

